I thought about it and just figured out a way to count $A$. Each element of $A$ is a finite set constructed of left brackets, $\{$, and right brackets, $\}$, so in replacing each left bracket with a $0$ and each right bracket with a $1$, we can convert each element of $A$ to a unique finite binary string:

Yup. I don't adhere to restricted comprehension (such as the axiom schema of specification, etc.) in defining $A$, but since $A$ is enumerable I don't see the point of doing so.

It matters not that I chose to apply a function to elements of the Alphabet as opposed to sets within the model. My definition is precise. Give me any set and we are able to tell precisely whether or not it is an element of $A$.

The difference between $L_{\omega}$ and $A$ as I understand it would be any infinite elements of $L_{\omega}$. That's it.

Not if you still don't get what $A$ is. At this point, that would be you. I'm not sure you know what $L_{\omega}$ is either at this point, though I'm asking because I myself would like clarification. I've noted that $L_{\omega} = V_{\omega}$ and I want to make sure I understand why.

Not if you still don't get what $A$ is. At this point, that would be you. I'm not sure you know what $L_{\omega}$ is either at this point, though I'm asking because I myself would like clarification. I've noted that $L_{\omega} = V_{\omega}$ and I want to make sure I understand why.

You haven't responded to any of my direct questions so there's not much left for me here.

I gave you the domain of $f$. What else did you ask that I haven’t given you?

It would be immensely helpful to me if you would go over each of my posts in this thread, and each time you see a sentence ending in '?', please give a clear, straightforward response in simple, declarative sentences. Don't add anything and don't assume anything. Just answer each question.

It would be immensely helpful to me if you would go over each of my posts in this thread, and each time you see a sentence ending in '?', please give a clear, straightforward response in simple, declarative sentences. Don't add anything and don't assume anything. Just answer each question.